The domination number of plane triangulations

Simon Spacapan

The domination number of plane triangulations

Combinatorics 2018-06-20 v1

Authors: Simon Spacapan

Abstract

We introduce a class of plane graphs called weak near-triangulations, and prove that this class is closed under certain graph operations. Then we use the properties of weak near-triangulations to prove that every plane triangulation on $n>6$ vertices has a dominating set of size at most $17n/53$ . This improves the bound $n/3$ obtained by Matheson and Tarjan.

Keywords

plane triangulation domination number weak near-triangulation dominating set graph theory

Cite

@article{arxiv.1806.06932,
  title  = {The domination number of plane triangulations},
  author = {Simon Spacapan},
  journal= {arXiv preprint arXiv:1806.06932},
  year   = {2018}
}

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